The Cornell potential in Lee-Wick inspired electrodynamics

Abstract: In the seventies, Lee and Wick proposed an interesting modification of classical electrodynamics that renders it finite at the quantum level. At the classical level, this modified theory leads to a regular linear potential at short distances while also reproducing the Coulomb potential at large distances. It is shown that a suitable modification of the Lee-Wick idea can also lead to a linear potential at large distances. For this purpose, we study an Abelian model that ``simulates" the QCD confining phase while maintaining the Coulomb behavior at short distances. This paper is organized in three parts. In the first part, we present a pedagogical derivation of the static potential in the Lee-Wick model between two heavy test charges using the Hamiltonian formulation. In the second part, we describe a modification of the Lee-Wick idea leading to the standard Cornell potential. In the third part, we consider the effect of replacing a point-like charge with a smeared Gaussian-type source, that renders the electrostatic potential finite as r--> 0.